List of series

From Simple English Wikipedia, the free encyclopedia

This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums.

Sums of powers[change | change source]

  • See also triangle number. This is one of the most useful series: many applications can be found throughout mathematics.
  • Where is the th Bernoulli number, is negative and is the binomial coefficient (choose function).
Where is the Riemann zeta function.

Power series[change | change source]

Infinite sum (for ) Finite sum
where and
where Lis(x) is the polylogarithm of x.

Simple denominators[change | change source]

Factorial denominators[change | change source]

Many power series which arise from Taylor's theorem have a coefficient containing a factorial.

  • (c.f. mean of Poisson distribution)
  • (c.f. second moment of Poisson distribution)

Modified-factorial denominators[change | change source]

Binomial series[change | change source]

Geometric series:

Binomial Theorem:

with generalized binomial coefficients

Square root:


  • [1]
  • [1]
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Binomial coefficients[change | change source]

Trigonometric functions[change | change source]

Sums of sines and cosines arise in Fourier series.

Unclassified[change | change source]

Related pages[change | change source]

Notes[change | change source]

  1. 1.0 1.1 1.2 1.3 Theoretical computer science cheat sheet

References[change | change source]